Nineteenth-century mathematics in the mirror of its literature: A quantitative approach

Abstract

The point of departure of this paper is the idea that the development of mathematics is reflected in its publications. Hence, the existence of a nearly complete database renders possible general statistical accounts of the development of mathematical activities. To this end, the authors utilize the mathematical index of the Catalogue of Scientific Papers of the Royal Society of London dealing with the mathematical journal literature of the 19th century. The relation between the journal and book literature of that century is discussed, with the result that the size of the journal literature is presumably a valid indicator of the intensity of mathematical activities in particular areas. On the basis of this Catalogue, graphs of the publication activity of all of 19th-century mathematics and of 34 of its most important subareas are displayed; both the number of active contributors in each area and its share of 19th-century mathematics publications are exhibited. Furthermore, the share of mathematics of the total scientific journal literature of the 19th-century is estimated. Frequency distributions of publication activity and the specialization of 19th-century mathematicians conform to patterns well known in modern scientometrics. © 1996 Academic Press, Inc.